The Joint Probability Density Function for Two Continuous Random Variables

The joint probability density function for two continuous random variables X and Y is $f ( x , y ) = \left\{ \begin{array} { l l } \frac { 1 } { 6 } e ^ { - x / 6 } e ^ { - y } & \text { if } x \geq 0 \text { and } y \geq 0 \\0 & \text { otherwise }\end{array} \right.$ Find the expected values $E ( X ) \text { and } E ( Y )$

A) $E ( X ) = 6 ; E ( Y ) = 1$
B) $E ( X ) = 1 ; E ( Y ) = 5$
C) $E ( X ) = 1 ; E ( Y ) = 6$
D) $E ( X ) = 7 ; E ( Y ) = 1$

Correct Answer:

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